Associative algebras with a distributive lattice of subalgebras

A. G. Gein

Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: We give a full description of associative algebras over an arbitrary field, whose subalgebra lattice is distributive. All such algebras are commutative, their nil-radical is at most two-dimensional, and the factor algebra with respect to the nil-radical is an algebraic extension of the base field.

Keywords: lattice of subalgebras, distributive lattice, lattice of subextensions of field.

UDC: 512.552.3

Received: 18.01.2020
Revised: 27.11.2020

DOI: 10.33048/alglog.2020.59.501

 English version: Algebra and Logic, 2020, 59:5, 349–356

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